The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  1  X  1  X  1  1  1  X  1  1  1  1  1  1  X  X  1  1  X  1  X
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  X 2X 2X  X 2X  X 2X  0  X  0 2X 2X  X 2X 2X 2X  0 2X  X  X  X  0  X  0  X  X  0  X 2X  X  X  X  X  X  0 2X  0 2X  0  0  X 2X  0 2X  X 2X  0
 0  0  X  0  0  0  0  0  0  0  0  X 2X 2X 2X 2X  0  X  X 2X 2X  X  X 2X  X  0  0  X  0 2X  X  X  X  0  0  0  X 2X  X  X 2X 2X  X 2X  0  X  0  0 2X  0  X  X  X  0  0  X  0  0 2X  X  X
 0  0  0  X  0  0  0  0  X 2X 2X 2X  0  0  X  0  X 2X 2X  0 2X  X 2X  X 2X  X  X  X  0  X  X  0 2X  X  X 2X  0  X  X  0  0  X  X  X  0  X  X  X  X  X 2X 2X  X 2X  0  0 2X  0 2X  X  0
 0  0  0  0  X  0  0  X 2X  0 2X  0  0 2X 2X  X  X  X  0  X  X 2X  X 2X 2X  0  X  X  X 2X 2X 2X  0  0  0 2X  0 2X 2X  X  X  0  0 2X  X 2X  0  X  0 2X 2X 2X 2X  X  X  X 2X  0  X  X 2X
 0  0  0  0  0  X  0 2X 2X  X  0 2X 2X 2X 2X 2X 2X  0  0  X  0 2X 2X 2X  X 2X  0 2X  X  X  X  0  0  0  0  0 2X  0 2X  X  0  X  X  0 2X  X  X 2X  X 2X  0  0  0  X  0  X 2X  X 2X  0  X
 0  0  0  0  0  0  X 2X 2X 2X 2X 2X 2X  X  X  X  0 2X  X 2X 2X 2X 2X  0  X 2X  X  X  X 2X 2X  X  X 2X  X  X  X  X 2X  X  X  0  X  0  0 2X 2X  X 2X 2X  X 2X  0 2X  X  0 2X 2X  X  0 2X

generates a code of length 61 over Z3[X]/(X^2) who´s minimum homogenous weight is 105.

Homogenous weight enumerator: w(x)=1x^0+98x^105+6x^107+178x^108+24x^110+234x^111+150x^113+206x^114+492x^116+180x^117+834x^119+206x^120+1176x^122+244x^123+1122x^125+176x^126+438x^128+148x^129+132x^131+140x^132+144x^135+90x^138+62x^141+44x^144+22x^147+6x^150+6x^153+2x^156

The gray image is a linear code over GF(3) with n=183, k=8 and d=105.
This code was found by Heurico 1.16 in 1.17 seconds.